The stability of an isolated vortex in a two-layer stably stratified fluid on a rotating plane (f-plane approximation) is studied. In the case of axially symmetric vortex structure consistent of a set of vortex patches, the problem of linear instability with respect to small disturbances of the patches’ boundaries may be solved analytically. Dispersion relationships allow studying the stability properties of the vortex, depending on the respective thickness of the layers, radii of the vortex patches, the medium stratification and the value of potential vorticity. Contour Dynamics Method (CDM) allows investigation of the non-linear stage in the evolution of unstable vortex structures, and, in particular, the time law of scattering of newly formed two-layer vortices of smaller size. When unstable vortices with zero total vorticity (heton) decays, the scattering is shown to follow the ballistic law. The obtained results can be used in the problems of deep convection for describing the process of spreading of heat and density anomalies. The use of CDM gives also possibility to examine the stability and peculiarities of the further evolution on non-axially symmetric vortex structures – the hetons with “tilted axis” and two-layer quasi-elliptical vortices.